import numpy linalg import numpy random from matplotlib import pyplot

  • Anonymous
  • Python
  • 05 Mar 2020 
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import numpy.linalg

import numpy.random

from matplotlib import pyplot as plt

import numpy as np

import matplotlib.path as path

from math import pi, cos, sin, atan, asin, fabs, sqrt





def ellipse_by_5_points(p):

    A = [[p[0][0] * p[0][1], p[0][1] * p[0][1], p[0][0], p[0][1], 1],

         [p[1][0] * p[1][1], p[1][1] * p[1][1], p[1][0], p[1][1], 1],

         [p[2][0] * p[2][1], p[2][1] * p[2][1], p[2][0], p[2][1], 1],

         [p[3][0] * p[3][1], p[3][1] * p[3][1], p[3][0], p[3][1], 1],

         [p[4][0] * p[4][1], p[4][1] * p[4][1], p[4][0], p[4][1], 1]]



    B = [[p[0][0] * p[0][0], p[0][1] * p[0][1], p[0][0], p[0][1], 1],

         [p[1][0] * p[1][0], p[1][1] * p[1][1], p[1][0], p[1][1], 1],

         [p[2][0] * p[2][0], p[2][1] * p[2][1], p[2][0], p[2][1], 1],

         [p[3][0] * p[3][0], p[3][1] * p[3][1], p[3][0], p[3][1], 1],

         [p[4][0] * p[4][0], p[4][1] * p[4][1], p[4][0], p[4][1], 1]]



    C = [[p[0][0] * p[0][0], p[0][0] * p[0][1], p[0][0], p[0][1], 1],

         [p[1][0] * p[1][0], p[1][0] * p[1][1], p[1][0], p[1][1], 1],

         [p[2][0] * p[2][0], p[2][0] * p[2][1], p[2][0], p[2][1], 1],

         [p[3][0] * p[3][0], p[3][0] * p[3][1], p[3][0], p[3][1], 1],

         [p[4][0] * p[4][0], p[4][0] * p[4][1], p[4][0], p[4][1], 1]]



    D = [[p[0][0] * p[0][0], p[0][0] * p[0][1], p[0][1] * p[0][1], p[0][1], 1],

         [p[1][0] * p[1][0], p[1][0] * p[1][1], p[1][1] * p[1][1], p[1][1], 1],

         [p[2][0] * p[2][0], p[2][0] * p[2][1], p[2][1] * p[2][1], p[2][1], 1],

         [p[3][0] * p[3][0], p[3][0] * p[3][1], p[3][1] * p[3][1], p[3][1], 1],

         [p[4][0] * p[4][0], p[4][0] * p[4][1], p[4][1] * p[4][1], p[4][1], 1]]



    E = [[p[0][0] * p[0][0], p[0][0] * p[0][1], p[0][1] * p[0][1], p[0][0], 1],

         [p[1][0] * p[1][0], p[1][0] * p[1][1], p[1][1] * p[1][1], p[1][0], 1],

         [p[2][0] * p[2][0], p[2][0] * p[2][1], p[2][1] * p[2][1], p[2][0], 1],

         [p[3][0] * p[3][0], p[3][0] * p[3][1], p[3][1] * p[3][1], p[3][0], 1],

         [p[4][0] * p[4][0], p[4][0] * p[4][1], p[4][1] * p[4][1], p[4][0], 1]]



    F = [[p[0][0] * p[0][0], p[0][0] * p[0][1], p[0][1] * p[0][1], p[0][0], p[0][1]],

         [p[1][0] * p[1][0], p[1][0] * p[1][1], p[1][1] * p[1][1], p[1][0], p[1][1]],

         [p[2][0] * p[2][0], p[2][0] * p[2][1], p[2][1] * p[2][1], p[2][0], p[2][1]],

         [p[3][0] * p[3][0], p[3][0] * p[3][1], p[3][1] * p[3][1], p[3][0], p[3][1]],

         [p[4][0] * p[4][0], p[4][0] * p[4][1], p[4][1] * p[4][1], p[4][0], p[4][1]]]



    a = numpy.linalg.det(A)

    b = -numpy.linalg.det(B)

    c = numpy.linalg.det(C)

    d = -numpy.linalg.det(D)

    e = numpy.linalg.det(E)

    f = -numpy.linalg.det(F)



    # I1 = a + c

    # I2 = a * c - (b / 2) ** 2

    # I3 = numpy.linalg.det([[a, b / 2, d / 2], [b / 2, c, e / 2], [d / 2, e / 2, f]])

    #

    # if I2 > 0 and I1 * I3 < 0:

    #     return [a, b, c, d, e, f]

    # else:

    #     return None

    return [a, b, c, d, e, f]





def rotate(A, B, C):

    return (B[0] - A[0]) * (C[1] - B[1]) - (B[1] - A[1]) * (C[0] - B[0])





def jarvismarch(A):

    n = len(A)

    P = [i for i in range(n)]

    for i in range(1, n):

        if A[P[i]][0] < A[P[0]][0]:

            P[i], P[0] = P[0], P[i]

    H = [P[0]]

    del P[0]

    P.append(H[0])

    while True:

        right = 0

        for i in range(1, len(P)):

            if rotate(A[H[-1]], A[P[right]], A[P[i]]) < 0:

                right = i

        if P[right] == H[0]:

            break

        else:

            H.append(P[right])

            del P[right]

    H = [A[H[i]] for i in range(len(H))]

    return H



def in_ellipse(p, koef):

   if koef[0] * p[0] ** 2 + koef[1] * p[0] * p[1] + koef[2] * p[1] ** 2 + koef[3] * p[0] + koef[4] * p[1] + koef[5] < 0:

       print(p)

       return True

   return False







def empty_ellipse(koefficient, points, ii):

        for i in points:

            if i not in ii:

                if in_ellipse(i, koefficient):

                    return False

        return True







def create_points(N):

    points = []

    while len(points) < N:

        new_p = [numpy.random.randint(-10, 10), numpy.random.randint(-10, 10)]

        if new_p not in points:

            points.append(new_p)

    return points





def empty_ellipses_into_5_points(points):

    empty_ellipses = []

    e_numbers = []

    for i1 in range(len(points)):

        for i2 in range(i1 + 1, len(points)):

            for i3 in range(i2 + 1, len(points)):

                for i4 in range(i3 + 1, len(points)):

                    for i5 in range(i4 + 1, len(points)):

                        conv = jarvismarch([points[i1], points[i2], points[i3], points[i4], points[i5]])

                        if (len(conv) == 5):

                            

                            koefficient = ellipse_by_5_points(conv)

                            if empty_ellipse(koefficient, points,[points[i1], points[i2], points[i3], points[i4], points[i5]]):

                                empty_ellipses.append(koefficient)

                                e_numbers.append([i1, i2, i3, i4, i5])

                                

    return empty_ellipses, e_numbers





def draw_ellipse(ellipse):

    a = ellipse[0]

    b = ellipse[1]

    c = ellipse[2]

    d = ellipse[3]

    e = ellipse[4]

    f = ellipse[5]

    matrix = np.mat([[c, b / 2], [b / 2, a]])

    w, ww = np.linalg.eig(matrix)

    ww = np.squeeze(np.asarray(ww))



    y0 = (d * b - 2 * a * e) / (4 * a * c - b * b)  # y-position of the center

    x0 = -(e + 2 * c * y0) / b  # x-position of the center



    k = ww[0][1] / ww[0][0]

    k1 = ww[1][1] / ww[1][0]



    r_2 = a * x0 * x0 + b * x0 * y0 + c * y0 * y0 - f



    delta_x = r_2 / (a + b * k + c * k * k)

    delta_y = k * k * delta_x



    ax = sqrt(delta_x + delta_y)



    delta_x = r_2 / (a + b * k1 + c * k1 * k1)

    delta_y = k1 * k1 * delta_x



    by = sqrt(delta_x + delta_y)

    t_rot = atan(k)  # rotation angle



    t = np.linspace(0, 2 * pi, 100)

    Ell = np.array([ax * np.cos(t), by * np.sin(t)])

    R_rot = np.array([[cos(t_rot), -sin(t_rot)], [sin(t_rot), cos(t_rot)]])



    Ell_rot = np.zeros((2, Ell.shape[1]))

    for i in range(Ell.shape[1]):

        Ell_rot[:, i] = np.dot(R_rot, Ell[:, i])



    plt.plot(x0 + Ell_rot[0, :], y0 + Ell_rot[1, :], 'darkorange')  # rotated ellipse





    # return [b / (2 * a), c / a]





points = create_points(7)

print(points)



empty_ellipses, e_numbers = empty_ellipses_into_5_points(points)

k = 0

for i in points:

    plt.plot(i[0], i[1], 'bo')

    plt.annotate(str("%d" % k), [i[0], i[1]])

    k = k + 1

plt.grid()

plt.axis([-11, 11, -11, 11], 'equal')

plt.gca().set_aspect("equal")

plt.show()



for ellipse in empty_ellipses:

    k = 0

    for i in points:

        plt.plot(i[0], i[1], 'bo')

        plt.annotate(str("%d" % k), [i[0], i[1]])

        k = k + 1

    plt.grid()

    plt.axis([-11, 11, -11, 11], 'equal')

    plt.gca().set_aspect("equal")

    draw_ellipse(ellipse)

    plt.show()

#plt.savefig('/home/kate/Рабочий стол/Figure_1.png')
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